Non-biased, centrally-cleared financial instrument and method of clearing and settling

ABSTRACT

In accordance with the principles of the present invention a non-biased, computer-implemented financial instrument electronic trading system and electronic central clearinghouse are provided. The electronic trading system and electronic central clearinghouse operate to provide electronic trading of financial instruments that are non-biased in that the electronic trading system and electronic clearing house address at least one of two effects that result from the difference between variation margin on a cleared financial instrument and collateral posted on an uncleared financial instrument, the first effect being a systematic advantage of being short the financial instrument when there is a correlation between the value of the financial instrument and interest rates, referred to as a convexity bias, and the second effect being a distortion in the financial instrument when an underlying asset value of the financial instrument changes, referred to as a net present value (NPV) effect.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.16/713,140, filed Dec. 13, 2019, entitled “Non-Biased, Centrally-ClearedFinancial Instrument and Method of Clearing and Settling,” which is acontinuation of U.S. patent application Ser. No. 15/731,589, filed Jul.5, 2017, entitled “Non-Biased, Centrally-Cleared Financial Instrumentand Method of Clearing and Settling,” now U.S. Pat. No. 10,586,284,which is a divisional of U.S. patent application Ser. No. 12/806,860,filed Aug. 23, 2010, now U.S. Pat. No. 9,747,641, entitled “Non-Biased,Centrally-Cleared Financial Instrument and Method of Clearing andSettling”, all of which are hereby incorporated by reference in theirentirety.

FIELD OF THE INVENTION

The present invention relates to financial instruments, and to theelectronic clearing and settling of such financial instruments.

BACKGROUND OF THE INVENTION

A variety of different types of financial instruments are tradedthroughout the world. Examples include cash contracts and derivatives. Acash contract is an agreement for either immediate or deferred deliveryof the specified asset. A derivative is a financial instrument whosevalue is linked to the price of an underlying commodity, asset, rate,index, currency or the occurrence or magnitude of an event. Typicalexamples of derivatives include futures, forwards, options, and swaps.

Most commonly, a swap is an agreement between two parties to exchangesequences of cash flows for a set period of time. Usually, at the timethe swap is initiated, at least one of these series of cash flows isbenchmarked to an asset or an index that is variable, such as aninterest rate, foreign exchange rate, equity price or commodity price. Aswap may also be used to exchange one security for another to change thematurity (bonds), quality of issues (stocks or bonds) or to facilitate achange in investment objectives.

A nomenclature has developed to describe the characteristics of certainswaps. A “plain-vanilla” swap is one that only has the simplest and mostcommon terms. A “spot” starting swap is one where the economics of theswap start almost immediately upon two parties entering into the swap. A“seasoned” swap is one that has been in existence for some time. A“forward-starting” swap is one where the first calculation date of theswap does not commence until a designated point in the future. Theparties to a forward-starting swap are still responsible for performingtheir obligations, but these obligations do not start for a period oftime after the parties have agreed to enter into the swap. An“off-market” swap is one that has a value other than zero at initiation.

The first swap occurred between IBM and the World Bank in 1981. Althoughswaps have only been trading since the early 1980's, they have explodedin popularity. In 1987, the swaps market had a total notional value of$865.6 billion; by mid-2006, this figure exceeded $250 trillion. That ismore than 15 times the size of the U.S. public equities market.

The most common type of swap is an interest-rate swap. In aplain-vanilla, interest-rate swap, two parties agree to exchangeperiodic interest payments, typically when one payment is at a fixedrate and the other varies according to the performance of an underlyingreference rate. Interest-rate swaps are generally quoted in yield terms.Conceptually, an interest-rate swap can be viewed as either a portfolioof forwards, or as a long (short) position in a fixed-rate bond coupledwith a short (long) position in a floating-rate bond. Commonly, for U.S.dollar denominated interest-rate swaps, the rate quoted is the fixedrate that the market expects will offset future 3-month London InterBankOffered Rate (LIBOR) (or whatever underlying reference rate is specifiedin the swap). (LIBOR refers to a daily reference rate based on theinterest rates at which banks borrow unsecured funds from other banks inthe London wholesale interbank market.) Cash then flows on a periodicbasis between the buyer and the seller depending on the differencebetween the fixed rate and the floating rate. For example, one party(Party A) agrees to pay another party (Party B) a predetermined, fixedrate of interest on a notional amount on specific dates for a specifiedperiod of time; concurrently, Party B agrees to pay Party A a floatinginterest rate on that same notional amount on the same specified datesfor the same specified time period. Interest payments may be madeannually, quarterly, monthly or at any other interval determined by theparties.

Standardized derivatives have traditionally been exchange-traded andcentrally-cleared financial instruments; swaps, on the other hand, havetraditionally been customized financial instruments that are traded inthe over-the-counter (OTC) market. (The OTC market most commonly refersto privately negotiated trades between two parties that are notcentrally cleared (i.e. uncleared).) Each party looks solely to theother party for performance and is thus exposed to the credit risk ofthe other party (often referred to as counterparty risk). Unlikefinancial instruments that are centrally cleared, there is noindependent guarantor of performance. Uncleared swaps are oftentransacted pursuant to International Swaps and Derivatives Association(ISDA) master documentation. The ISDA, 360 Madison Avenue, 16th Floor,New York, N.Y. 10017 is an association formed by the privatelynegotiated derivatives market that represents participating parties.

It is common for collateral to change hands as the value of an unclearedposition changes. The party that has an unrealized loss on an open,uncleared position will post collateral with the party that has theunrealized gain in order to secure its liability. A common form ofcollateral is obligations of the United States Treasury (i.e. TreasuryBonds, Notes, and Bills). When a Treasury obligation is posted ascollateral, price changes in that financial instrument and couponpayments accrue to the owner of the collateral, that being the partyposting the financial instrument. Cash may also be posted as collateral,in which case the party receiving the cash as collateral is obligated topay interest to the party posting the cash collateral at a rate set byagreement between the parties. When the trade is unwound or expires, theparty holding the collateral returns it to the other party, and thetrade is ultimately settled.

Financial instruments traded on exchanges are distinctly different fromuncleared financial instruments. While the economics of the two may besimilar, futures and options on futures (futures options) are traded onand pursuant to the rules of an exchange. Unlike uncleared financialinstruments where the parties set the terms of the trade,exchange-listed futures and futures options are standardized. Such termsinclude notional amount, price change per increment, expiration date,and how the financial instrument is settled (either cash settlement orphysical delivery) at expiration. The only matters for parties tonegotiate in futures, other than which party is the buyer and whichparty is the seller, is the number of financial instruments to be tradedand the price.

All futures and futures options are centrally cleared. This is quitedifferent from uncleared financial instruments discussed above. Centralclearing means that the counterparty risk is removed. The parties to atrade cease to be counterparties to each other; rather, each party facesa clearinghouse and looks solely to the clearinghouse for performance.(A clearinghouse is an agency of an exchange or separate entityresponsible for settling trading accounts, clearing trades, collectingand maintaining margin, regulating delivery and reporting trading data.)

Recently, there has been a trend for OTC financial instruments to becentrally cleared. In certain circumstances, parties to an OTC financialinstrument can submit the financial instruments to a clearinghouse forcentral clearing. Once the trade is accepted by a clearinghouse, thecounterparty risk is eliminated, and each party then faces theclearinghouse. For example, on the Chicago Mercantile Exchange Group's(CME), ClearPort facility, 20 South Wacker Drive, Chicago, Ill. 60606,OTC trades in certain financial instruments may be converted intofutures or futures options, as the case may be, upon acceptance by CME'sclearinghouse. In effect, these “OTC” financial instruments go through atransformation into futures or futures options. Other financialinstruments may be accepted by a clearinghouse for central clearing, butdo not convert into futures and remain customized. In these cases, likeall centrally-cleared financial instruments, the counterparty risk isstill eliminated.

The method by which clearinghouses treat margin on cleared financialinstruments (including futures and non-standardized financialinstruments accepted for central clearing) is considerably differentfrom the uncleared norm. For both cleared and uncleared financialinstruments there are two forms of margin: initial margin and variationmargin. For a cleared financial instrument, both parties must postinitial margin in an amount set by the clearinghouse upon initiation ofa position and maintain that initial margin as long as the position isheld. For an uncleared financial instrument, only one party (but notboth as in cleared financial instruments) may be required to postinitial margin (known as collateral for uncleared financialinstruments). In the case of cleared and uncleared financialinstruments, a party posting this collateral generally continues to earninterest on cash posted or, if a Treasury instrument is posted,continues to have the right to the coupons generated by the Treasuryinstrument and accrues the gains or losses from any change in the valueof the Treasury instrument.

For variation margin, there is a dramatic difference between thetreatment depending on whether the trade is cleared and uncleared. Inboth cases, margin moves as the marked-to-market value of the positionchanges. (Marked-to-market value reflects the current value of afinancial instrument rather than its book value.) This movement ofmargin generally occurs on a daily basis. If a party receives variationmargin by virtue of a profitable position in a cleared financialinstrument, that party is the owner of the margin and may do whatever itchooses with such margin. On the other hand, in uncleared financialinstruments, the party posting cash or Treasury instruments ascollateral receives the interest on the cash posted or the coupon fromthe Treasury instrument and accrues the gains or losses from any changein the value of the Treasury instrument (if such a Treasury instrumentis posted in lieu of cash).

There are two important effects that result from the difference in thetreatment of variation margin between cleared and uncleared positions:the first effect is commonly known as the “convexity bias”, and thesecond effect will be referred to herein as the “NPV effect”. Withrespect to the convexity bias, assume a party establishes a shortposition in a Eurodollar future listed on the CME. Eurodollar futuresare based on the 3-month LIBOR interest rate. The final settlement valuefor Eurodollar futures is equal to 100 minus the 3-month LIBOR rate. Asinterest rates rise, the price of Eurodollar futures decline. Furtherassume that shortly after establishing the position, the trade becomesprofitable on a marked-to-market basis due to an increase in interestrates. As a result, the party receives variation margin in the form ofcash equal to the profit. The party could now use the variation marginto purchase a zero-coupon Treasury bond.

Now assume that interest rates subsequently decline to where they wereinitially. This results in a payment of variation margin being due—equalto the initial amount received. The party is now in the same position asbefore the change in interest rates with respect to the futures profitand loss; however, because interest rates are now lower than they werewhen the zero-coupon bond was purchased, the party will realize a profiton the bond when liquidating it. Hence, there is a clear benefit tobeing short Eurodollar futures because of the positive correlationbetween the underlying futures and fixed- income instruments in general.As a result, Eurodollar futures trade at higher yields (lower prices)than related uncleared financial instruments, including interest-rateswaps.

If the underlying asset for the future was natural gas (rather than3-month LIBOR), then the different treatment of cleared as compared touncleared collateral schemes would not result in any significant benefitto being short (or long) futures as a result of the convexity bias. Thisis because there is generally little correlation between the price of azero coupon bond and the price of natural gas, and the convexity biasonly takes effect when such correlation is high.

In the example of Eurodollar futures, the benchmark underlying thefuture is 3-month LIBOR. There is a very high positive correlationbetween a zero coupon bond and a Eurodollar future. As first recognizedin the early 1990's, this results in a fundamental benefit from beingshort exchange-traded, interest-rate futures relative to uncleared OTCinterest-rate swaps, introducing what is known as a convexity bias inthe pricing of interest-rate futures. See Burghardt and Hoskins, “TheConvexity Bias in Eurodollar Futures: Part 1”, 1 Derivatives Quarterly47 (Spring 1995); Burghardt and Hoskins, “The Convexity Bias inEurodollar Futures: Part 2”, 59 Derivatives Quarterly 72 (Summer 1995).Unless addressed, the convexity bias exists for any financial instrumentthat is cleared where there is a correlation between the value of thefinancial instrument and interest rates.

In more detail, as noted by Burghardt and Hoskins: “There is asystematic advantage to being short Eurodollar futures relative todeposits, swaps, or FRAs [Forward Rate Agreements]. Because of thisadvantage, which we characterize as a convexity bias, Eurodollar futuresprices should be lower than their so-called fair or proper values. Putdifferently, the 3-month interest rates implied by Eurodollar futuresprices should be higher than the 3-month forward rates to which they aretied.”

Because there is a high correlation between the yield of aninterest-rate swap and interest rates, the convexity bias is highlyrelevant in determining the value of cleared interest-rate swaps andinterest-rate swap futures. The value of the convexity bias is dependenton a number of factors, including the correlation and the volatility ofthe relevant asset. Under current market conditions, for a convexitybiased cleared 10 year dollar denominated vanilla interest-rate swap,the bias is worth approximately 25 basis points (0.25%). It is importantto note that when Burghardt and Hoskins first wrote about the convexitybias, interest-rate swaps were not cleared financial instruments.

The second effect that results from the difference between variationmargin on a cleared financial instrument and collateral posted in anuncleared financial instrument will be referred to herein as the “NPVeffect”. While the NPV effect and the convexity bias are intertwined,cleared financial instruments that have no correlation to interest ratesstill will be subject to the NPV effect, though not subject to aconvexity bias.

The following example illustrates the NPV effect. Assume that a party toa 10-year, natural-gas swap makes fixed monthly payments of $4 (thebuyer of the swap), and receives floating payments equal to the spotprice of natural gas from a counter party (the seller). Because this isa 10-year swap, these payments continue for 120 consecutive months.Assume further that on the date the swap was created, the 10-year,natural-gas forward curve is flat at $4. Therefore, the swap requires noupfront payments. On the day after the parties enter into the swap, the10-year, natural-gas forward curve moves to a flat $5. At that point,the buyer expects to receive $1 every month for the next 10 years, or$120 over the next 10 years. The net present value of these cash flows,assuming a 6.0% annual interest rate, is approximately $90. Because ofthe assumed lack of correlation between the price of natural gas andinterest rates in general, the convexity bias does not exist.

In the case of an uncleared natural-gas swap, the buyer receives $90,the net present value of the future cash flows, as collateral from theseller. If the buyer unwinds the trade by selling the swap to a thirdparty for fair value, an upfront payment of $90 will be made to theoriginal buyer, and the $90 collateral will be transferred to the thirdparty. The original buyer has thus realized a profit of $90 and hasliquidated its position.

Now consider a cleared natural-gas swap without any adjustments for theNPV effect. When the natural-gas forward curve moves to $5, the fairvalue settlement price of the cleared swap is $120, the sum of futurecash flows. This is because futures by arbitrage-fee principle trade attheir future value. Therefore the buyer receives $120 of variationmargin today, as opposed to $90 in the uncleared case. The buyer couldnow exit or hedge off the position, and would be materially better offthan had an uncleared swap been traded. This difference is caused bywhat is referred to herein as the NPV effect. Note that as interestrates approach zero, the NPV effect is eliminated.

Some exchanges and clearinghouses attempt to address this issue byrequiring the swap to settle as if it were economically equivalent to anuncleared swap. In this case, the daily settlement price is defined asthe net present value of the future cash flows. While this gives theimpression that it solves the NPV effect, it does not: this creates aswap that is neither equivalent to a cleared nor an uncleared swap.Continuing with the example, if the swap is required to settle at $90after the move of the natural-gas forward curve to $5, the buyerreceives $90 of variation margin. Now assume that the buyer sells theposition to a third party. If the buyer sells the position for the newsettlement price, and keeps the $90 of variation margin, then it wouldbe in the same place as if it had traded an uncleared swap. But the newbuyer will receive a windfall profit. The new buyer could hedge off thenatural-gas price risk by entering into an offsetting, 10-year, $5natural-gas swap, and receive $30 over the next 10 years. Clearly theexistence of this risk-free profit demonstrates that the cleared swaptraded at the settlement price of $90 was transacted at something otherthan fair value. In fact, to consummate the trade at fair value thethird party must pay the original buyer the present value of this $30,or approximately $22 under our 6.0% assumed interest rate.

The above example demonstrates that the cleared swap, without anappropriate adjustment, generates a different profit and loss from theuncleared swap when the underlying asset value, the price of natural gasin the example, changes. Furthermore, the example uncovers a potentialrisk to the clearinghouse that, when the settlement methodologies arenot properly delineated, the marked-to-market price may not reflect theactual fair value of the financial instrument. Because central clearingof swaps is relatively new, this effect is not widely known orunderstood.

The NPV effect also exists with respect to cleared credit default swaps(CDS). In a CDS, the protection buyer makes a series of payments to theprotection seller, and in exchange the protection buyer receives apayment if the “reference entity”, usually a corporation or government,defaults. A default includes such events as failure to pay,restructuring, and bankruptcy. In addition to the NPV effect, because ofa correlation between the interest rate in general and the default ratea centrally-cleared CDS may have a convexity bias relative to anuncleared CDS. This convexity bias tends to be much smaller than in thecase of interest-rate swaps. See, for example, Kaplin, Qu, Wang, Wang,and Zhang, “The Relationship Between Default Risk and Interest Rates: AnEmpirical Study”, Moody's Analytics (2 Oct. 2009) (available athttp://www.moody skmv.com/ research/files/Default_and_Interest_Rates.pdf(accessed 18 Aug. 2010); Chen, Cheng, Fabozzi, and Liu, “An Explicit,Multi-Factor Credit Default Swap Pricing Model with Correlated Factors”,43 Journal of Financial & Quantitative Analysis 123 (March 2008)(available at http://www.bnet.fordham.edu/rchen/jfqa-final.pdf)(accessed 18 Aug. 2010).

One attempt to simultaneously address the convexity bias and the NPVeffect was the introduction of the “Price Alignment Interest” (PAI) in2008 on the SwapClear Facility of LCH.Clearnet, Aldgate House, 33Aldgate High Street, London EC3N 1EA U.K. (LCH.Clearnet is anindependent clearinghouse serving exchanges and trading platforms, aswell as a range of OTC markets. SwapClear is a service for the centralclearing of OTC interest-rate swaps.) Counterparties initially enterinto a bilateral interest-rate swap and subsequently submit the swap forclearing through LCH.Clearnet. Upon acceptance of the swap byLCH.Cleamet, the parties to the trade cease to be counterparties to eachother and each faces LCH.Clearnet and looks solely to LCH.Clearnet forperformance.

LCH.Cleamet introduced PAI to eliminate the convexity bias and the NPVeffect. As noted in the LCH.Clearnet rules, “The payment of variationmargin, or change in NPV [net present value], on a daily basis withoutadjustment would distort the pricing for swaps cleared through theClearing House.” LCH.Clearnet Rule 2C.6.4. To attempt to address thisdistortion, LCH.Clearnet charges interest on cumulative variation marginreceived and pays interest on cumulative variation margin paid.

However, PAI is not a viable solution for systems that process clearedfinancial instruments, including futures. As noted above, variationmargin on a cleared position is currently calculated by marking aposition to market. This calculation is undertaken on the basis ofthen-existing market prices, without regard to any convexity bias or NPVeffect. The addition of PAI would require the calculation and processingof a separate and distinct form of variation margin. Unfortunately, thesystems currently used by traditional futures clearinghouses, exchanges,brokers, and other market participants for calculating variation marginare not equipped to incorporate this additional calculation. Significantchanges would be required across the industry to include PAI in thecalculation of variation margin for cleared swaps, and it would be verydifficult for the industry to adapt to such a methodology in areasonable time frame.

While swaps have traditionally been uncleared, recently there has beenpressure to migrate swaps to central clearing, including mandates setforth in the Dodd-Frank Wall Street Reform and Consumer Protection Act(the “Dodd-Frank Act”) (Pub.L. 111-203, H.R. 4173) signed into law byPresident Obama on 21 Jul. 2010. As a result of political pressure forgreater transparency of uncleared financial instruments, the Dodd-FrankAct was passed into law in the wake of the 2008/2009 financial crisis.During the 2008/2009 financial crisis, many participants in unclearedfinancial instruments faced counterparties that were unable to meettheir obligations.

One such effort to migrate swaps to an exchange and central clearing isthe formation of Eris Exchange, an exempt board of trade. As reported bythe Financial Times, Eris Exchange “will offer trading in interest-rateswap derivatives closely modeled on current over-the-counter (OTC) rateswaps”. Grant, Weitzman, and Mackenzie, “Chicago Traders Launch NewDerivatives Exchange” Financial Times (13 Jul. 2010). The CME'sclearinghouse will be the central clearer of interest-rate swapderivatives traded on Eris Exchange. “After the details of the swap,like notional value, coupon, and maturity are agreed to, the Exchangepasses the new trade to the Clearing House where it is processed like atraditional futures contract.” http://www.erisweb.com (accessed 17 Aug.2010).

Unless addressed, the convexity bias and the NPV effect will in mostcases result in significant pricing discrepancies betweencentrally-cleared interest-rate swaps and interest-rate swap futures onthe one hand and uncleared interest-rate swaps on the other hand. As aresult, the cleared swaps will trade at significantly different yieldsthan the uncleared equivalent. At the very least, the convexity bias andthe NPV effect could create a serious impediment to the migration ofinterest-rate swaps to Eris Exchange, or to any other exchange or tocentral clearing, including, for example, interest-rate swaps clearedthrough the International Derivatives Clearing Group, LLC (IDCG), 150East 52nd Street, 5th Floor, New York, N.Y. 10022 or the CME.

Take the example of an exchange-cleared, $100M, 10-year, interest-rateswap traded at par (i.e. the coupon is set equal to the expected futureLIBOR rates over the term of the interest-rate swap). Because this swapis cleared, without an adjustment for the convexity bias, it would ithave to be traded at a significantly different yield than an unclearedswap with similar terms or arbitrage opportunities would exist. Assumingthat the convexity bias of a 10-year swap is 25 basis points, when theexchange-traded swap trades at a yield of 2.31, the equivalent yield ofa traditional, uncleared, interest-rate swap with similarcharacteristics and terms would be 2.56. In this example, the 25 basispoint difference in yields is worth approximately $2,000,000.Furthermore, the NPV effect will create an additional discrepancybetween the cleared and uncleared interest-rate swap when theinterest-rate yield curve changes such that the fair value of the swapchanges. If not addressed properly, these discrepancies resulting fromthe convexity bias and the NPV effect will create significant confusionand serious impediment to the migration of interest-rate swaps tocentral clearing and exchange-traded environments.

It would therefore be desirable to offer tools that adequately addressthe convexity bias and the NPV effect. It would be further desirable tohelp enable the migration of uncleared swaps and other unclearedfinancial instruments that are subject to the convexity bias and the NPVeffect to exchanges and central clearing to eliminate counterparty risk,whereby the parties to a trade can look solely to a clearinghouse forperformance, and to provide for greater transparency.

SUMMARY OF THE INVENTION

The present invention provides financial tools that address theconvexity bias and the net present value (NPV) effect. The presentinvention facilitates the migration of uncleared swaps and otheruncleared financial instruments that are subject to the convexity biasand/or the net present value (NPV) effect to exchanges and centralclearing to eliminate counterparty risk, whereby the parties to a tradelook solely to a clearinghouse for performance, and for greatertransparency.

In accordance with the principles of the present invention, computerimplemented, back-office method of creating, centrally clearing, andsettling a non-biased, financial instrument, through an electronictrading platform and an electronic central clearinghouse to effectuatepayments between parties to a trade is provided. A non-biased, financialinstrument in accordance with the principles of the present invention isto be centrally cleared and settled and can be traded either on or offan exchange or trading platform. The non-biased financial instruments towhich the present invention applies include, but are not limited to,interest-rate swaps, interest-rate swap futures, credit default swaps,credit default swap futures, other interest rate futures, forward rateinstruments, commodity swaps, total-return swaps, total-return swapfutures, variance swaps, variance-swap futures, cross-currency swaps,cross-currency swap futures, foreign-exchange swaps, andforeign-exchange swap futures, regardless of the currency in which thenon-biased financial instrument is denominated.

In accordance with the principles of the present invention, the computerimplemented, back-office method of creating, centrally clearing, andsettling a non-biased financial instrument through an electronic tradingplatform and an electronic central clearinghouse defines a terminalvalue in a way that offsets the co-movement of variation margin andinvestment return on the variation margin, during the life of thefinancial instrument. For example, in the case of an interest-rate swap,the terminal value comprises an accumulated value of payments madepursuant to the terms of the interest rate swap, minus the accumulatedvalue of interest earned on variation margin over the life of theinterest-rate swap. By addressing the convexity bias and the net presentvalue (NPV) effect, the non-biased, centrally-cleared interest-rate swapis functionally equivalent in economic terms to an unclearedinterest-rate swap.

BRIEF DESCRIPTION OF THE DRAWING

FIG. 1 is a flow-chart setting forth an example for determining the netaccumulated value of cash flows for a terminal value of a non-biased,centrally-cleared financial instrument of the present invention.

FIG. 2 is a flow-chart setting forth an alternative example fordetermining the terminal value of a non-biased, centrally-clearedfinancial instrument of the present invention.

FIG. 3 is a non-limiting example of a hardware infrastructure that canbe used to run a system that implements electronic clearing and settlingof the non-biased, centrally-cleared financial instrument of the presentinvention.

DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT

While an exemplary embodiment of the invention illustrated and describedhas been built to trade on Eris Exchange, it will be appreciated thatthe present invention is not so limited and can be cleared on anyclearinghouse, traded on other exchanges or trading platforms,regardless of whether located in. the United States or abroad, tradedthrough a private negotiation, traded in currencies other than UnitedStates dollars or traded as a future or as a cleared swap or other typeof financial instrument. When used herein, the terms exchange andtrading platform refer broadly to a marketplace in which securities,commodities, derivatives and other financial instruments are traded, andincludes but is not necessarily limited to designated contract markets,exempt boards of trade, designated clearing organizations, securitiesexchanges, swap execution facilities, electronic communicationsnetworks, and the like.

As previously detailed, given the differences in the manner in whichcollateral is treated in uncleared financial instruments on the one handand centrally-cleared financial instruments on the other hand, acentrally-cleared swap that is subject to the convexity bias and/or theNPV effect, whether traded as a future or otherwise, will, unlessaddressed, trade at a different value than the same swap that isuncleared. This could significantly impair the migration of swaps andother financial instruments that have traditionally not been cleared,particularly interest-rate swaps, to central clearing. The presentinvention provides a financial instrument that is economicallyequivalent to uncleared financial instruments, including swaps, thusfacilitating the migration of uncleared financial instruments tocentralized exchanges and/or to central clearing.

In accordance with the principles of the present invention, acentrally-cleared financial instrument is provided that addresses theconvexity bias and the NPV effect The non-biased, centrally-clearedfinancial instrument of the present invention is to be centrally clearedand can be traded either on or off an exchange or trading platform,whether traded as a future or other type of financial instrument. Whenused herein, non-biased refers to addressing the convexity bias or theNPV effect or both. The financial instruments to which the presentinvention applies include, but are not limited to, interest-rate swaps,interest-rate swap futures, credit default swaps, credit default swapfutures, other interest-rate futures, FRAs, commodity swaps, andforeign-exchange swaps, regardless of the currency in which thefinancial instrument is denominated.

As the convexity bias arises from the correlation between the value ofthe cleared financial instrument and fixed-income instruments ingeneral, a non-biased, centrally-cleared financial instrument of thepresent invention defines its terminal value (i.e. the final settlementvalue of the financial instrument upon its stated expiration) in a waythat offsets the co-movement of variation margin and the investmentreturn on the variation. margin during the life of the financialinstrument. In one embodiment in accordance with the principles of thepresent invention, the non-biased, centrally-cleared financialinstrument is a swap that defines its terminal value to be the netaccumulated value of the payments of the swap, minus the accumulatedvalue of interest on variation margin over the life of the swap. Theaccumulated value of payments includes coupon payments and compoundedinterest earned on coupon payments. When used herein, the term swap isused in a broad, functional sense, and is not meant to be limited to anyparticular regulatory or legal definition thereof.

In the example of an interest-rate swap, if interest rates increase, allelse being constant, the yield on the interest-rate swap will go up, or,in the alternative, if the interest-rate swap is traded in price terms,the price of the interest-rate swap will go down. Assuming thisinterest-rate swap is centrally cleared and traded in price terms, ashort position will have a positive cash flow from the variation marginwhen interest rates increase. Unless the convexity bias is addressed,the party holding the short position will be able to invest thevariation margin for a higher return as a result of the correlationbetween the interest-rate swap and interest rates in general. In thiscase, a non-biased, centrally-cleared financial instrument of thepresent invention will adjust the final payment of the financialinstrument to account for the convexity bias and make the clearedfinancial instrument of the present invention equivalent in economicterms to an uncleared interest-rate swap.

Subtracting the accumulated value of interest on variation margin fromthe terminal value of a financial instrument of the present inventionaddresses the NPV effect. Assume the expected net cash flow of a swapincreases due to a change in the value of the underlying asset, rate,commodity or index. Without the adjustment, the proper marked-to-marketvalue of a cleared swap will increase by an amount equal to the sum ofthe expected change in the future cash flows. In the case of a clearedswap, this amount is paid to the buyer at the end of the day throughvariation margin. A non-biased, centrally-cleared financial instrumentof the present invention decreases the terminal value of the financialinstrument by an amount equal to the total interest earned on theaccumulated variation margin over the life of the financial instrument,negating the NPV effect. Furthermore, setting the convexity bias aside,a non-biased, centrally-cleared financial instrument of the presentinvention will have a change in its fair value equal to the change inthe sum of the present value of the expected future cash flows, whichcoincides with the profit (loss) of an uncleared swap position.

When a swap is traded, regardless of whether it is an exchange-tradedswap future, a cleared swap or a traditional, uncleared swap, all of theterms of the fixed and floating payments are agreed upon at the time thetrade is consummated. When the financial instrument is anexchange-traded swap future or a centrally-cleared swap, the position ismarked to market periodically, most commonly daily, and variation marginflows based on the marked-to-market settlement. In one embodiment, theterminal value of a non-biased, centrally-cleared financial instrumentof the present invention can be determined as follows:

terminal  value = net  accumulated  value  of  cash  flows − total  return  on  variation  margin;

where,

-   -   net accumulated value of cash flows is the accumulated value        that a buyer (seller) of a financial instrument receives minus        the payments the buyer (seller) makes, reinvested at the        overnight rate from the date that the cash flow occurs to        expiration of the financial instrument;    -   total return on variation margin is the sum of the interest        earned on the cumulative variation margin for each day        reinvested at the overnight rate to expiration of the financial        instrument; and    -   the overnight rate is the rate specified by the exchange or        clearinghouse to reflect the short-term financing rate of market        participants.

The net accumulation of cash flows reinvested at the overnight rate overthe life of the non-biased, centrally-cleared financial instrument ofthe present invention is necessary to make the financial instrument ofthe present invention equivalent to an uncleared financial instrumentwith similar terms. A party who enters into an uncleared interest-rateswap is able to invest cash received from the coupon payments daily atthe overnight rate. When the party is obligated to make coupon paymentsunder such a swap, the party will pay interest on any funds borrowed tomake such payments or forego earning interest. The inclusion of the netaccumulated value of cash flows in the definition of terminal value ofthe non-biased, centrally-cleared financial instrument of the presentinvention replicates the cash flows associated with the unclearedfinancial instrument.

The other component of the definition of the terminal value of thenon-biased, centrally-cleared financial instrument of the presentinvention is the total return on variation margin. This adjustmentaddresses both the convexity bias and the NPV effect in a clearedfinancial instrument. While the adjustment achieves the same effect asLCH.Clearnet's Price Alignment Interest (PAI) by building the value intothe final settlement price without managing the PAI cash flow on a dailybasis, the current systems used to process traditional futures andcleared financial instruments will not need to change in order to handlea financial instrument created under the principles of the presentinvention. The PAI requires daily cash adjustments that the currentsystems for processing futures cannot handle. The present invention issuperior in that regard and will facilitate the migration of unclearedswaps and other uncleared financial instruments to central clearing andto centralized marketplaces.

In another embodiment in accordance with the present invention, aconstant can be added or subtracted to the above terminal valuedefinition. Adding or subtracting a constant to the above terminal valuedefinition may sometimes be preferable in order to be consistent withcertain market conventions. Generally the profit and loss of a clearedfinancial instrument comes only from the price change, and, thus,modifying the price process by a constant does not change the nature ofthe financial instrument.

Referring to FIG. 1, a flow-chart of an example embodiment fordetermining the net accumulated value of cash flows for the terminalvalue of a non-biased, centrally-cleared financial instrument of thepresent invention is seen. In the case of an interest-rate swap, thenon-biased, centrally-cleared financial instrument of the presentinvention would have the fixed rate as its coupon, and the term of theswap defines its expiration. Taking into account these factors, the netaccumulated value of cash flows can specifically be determined asfollows:

${{net}\mspace{14mu}{accumulated}\mspace{14mu}{value}\mspace{14mu}{of}\mspace{14mu}{cash}\mspace{14mu}{flows}} = {{\sum\limits_{i = 1}^{N}{C_{i}{B\left( {t_{c,i},T} \right)}}} - {\sum\limits_{i = 1}^{M}{L_{i}{B\left( {t_{l,i},T} \right)}}}}$

where,

-   -   C_(i) is the amount of fixed leg payment payable at time        t_(c,i);    -   L_(i) is the amount of the floating leg payment payable at time        t_(i,j);    -   T is the expiration of the financial instrument; and    -   B(t ,T) is the value of the money market account at time T with        an initial deposit of 1 at time t and accumulated at overnight        rate.

And total return on variation margin can be determined as:

${{{total}\mspace{14mu}{return}\mspace{14mu}{on}\mspace{14mu}{variation}\mspace{14mu}{margin}} = {\sum\limits_{t = 1}^{T - 1}{P_{t}R_{t}{B\left( {{t + 1},T} \right)}}}},$

where

-   -   P_(t) is the settlement price of the financial instrument on day        t, and    -   R_(t) is the overnight interest rate on day t.        Here we assume, without loss of generality, the initial trading        price is zero.

Referring to FIG. 2, a flow-chart of an alternative example embodimentfor determining the terminal value of a non-biased, centrally-clearedfinancial instrument of the present invention is seen. In thisalternative determination of the terminal value, which is equivalent tothe embodiments above, the terminal value can be determined as follows:

terminal  value = net  summation  of  cash  flows − total  return  on  modified  variation  margin,

where, using the previous notations,

${{{net}\mspace{14mu}{summation}\mspace{14mu}{of}\mspace{14mu}{cash}\mspace{14mu}{flows}} = {{\sum\limits_{i = 1}^{N}C_{i}} - {\sum\limits_{i = 1}^{M}L_{i}}}};{{{and}\mspace{14mu}{total}\mspace{14mu}{return}\mspace{14mu}{on}\mspace{14mu}{modified}\mspace{14mu}{variation}\mspace{14mu}{margin}} = {\sum\limits_{t = 1}^{T - 1}{\left( {P_{t} - \left( {{\sum\limits_{i:{({i_{c,i} < t})}}C_{i}} - {\sum\limits_{i:{({t_{i,i} < t})}}L_{i}}} \right)} \right)R_{t}{B\left( {{t + 1},T} \right)}}}}$

By rearranging the terms of the second terminal value definition, theequivalence of the two alternative definitions discussed above can beseen:

${{\sum\limits_{i = 1}^{N}C_{i}} - {\sum\limits_{i = 1}^{M}L_{i}} - {\sum\limits_{t = 1}^{T - 1}{\left( {P_{t} - \left( {{\sum\limits_{i:{({i_{c,i} < t})}}C_{i}} - {\sum\limits_{i:{({t_{i,i} < t})}}L_{i}}} \right)} \right)R_{t}{B\left( {{t + 1},T} \right)}}}} = {{\left( {{\sum\limits_{i = 1}^{N}C_{i}} + {\sum\limits_{t = 1}^{T}{\sum\limits_{i:{({i_{c,i} < t})}}{C_{i}R_{t}{B\left( {{t + 1},T} \right)}}}}} \right) - \left( {{\sum\limits_{i = 1}^{M}L_{i}} + {\sum\limits_{t = 1}^{T}{\sum\limits_{i:{({i_{c,i} < t})}}{L_{i}R_{t}{B\left( {{t + 1},T} \right)}}}}} \right) - {\sum\limits_{t = 1}^{T}{P_{t}R_{i}{B\left( {{t + 1},T} \right)}}}} = {{{\sum\limits_{i = 1}^{N}{C_{i}\left( {1 + {\sum\limits_{t = t_{c,i}}^{T}{R_{t}{B\left( {{t + 1},T} \right)}}}} \right)}} - {\sum\limits_{i = 1}^{M}{L_{i}\left( {1 + {\sum\limits_{t = t_{t,i}}^{T}{R_{t}{B\left( {{t + 1},T} \right)}}}} \right)}} - {\sum\limits_{t = 1}^{T}{P_{t}R_{t}{B\left( {{t + 1},T} \right)}}}} = \left( {{\sum\limits_{i = 1}^{N}{C_{i}{B\left( {t_{c,i},T} \right)}}} - {\sum\limits_{i = 1}^{M}{L_{i}{B\left( {t_{i,i},T} \right)}}} - {\sum\limits_{t = 1}^{T}{P_{t}R_{t}{B\left( {{t + 1},T} \right)}}}} \right)}}$

The following are non-limiting examples of non-biased, centrally-clearedfinancial instruments created by adjusting the terminal value for theinterest on variation margin in accordance with the principles of thepresent invention. In each example, the overnight rate is assumed to beequal to the yield on the applicable day. The discussion and the Tablesset forth below are from the perspective of the buyer of the financialinstrument unless otherwise noted.

EXAMPLE 1

This example shows that a non-biased, centrally-cleared financialinstrument in accordance with the present invention can replicate theprofit and loss of a spot-starting, uncleared interest-rate swap eachday. Consider a 10-year OTC swap with $100M notional value with a parcoupon of 2.0%. The buyer will receive 2.0% semi-annual interestpayments on the notional amount and pay 3-month LIBOR interest paymentson the notional amount quarterly.

A non-biased, centrally-cleared financial instrument in accordance withthe present invention can be created to replicate such a swap. Thisnon-biased, centrally-cleared swap has a 2.0% coupon, 10 years tomaturity. Suppose the yield changes to 2.1% on day 2. The followingTable 1 compares the performance of an uncleared, interest-rate swap anda non-biased, centrally-cleared swap position for the first few days:

TABLE 1 Performance of an Uncleared Swap and a Non-Biased SwapNon-Biased, Uncleared Centrally-Cleared Swap Swap Return on Total P&L toVariation Total P&L to Date Yield Date* Value** Margin**** Date*** 1 2.00 0 0 0 2 2.1 −906,497 −906,497 0 −906,497 3 2.1 −906,550 −906,497 −53−906,550 4 2.1 −906,603 −906,497 −53 −906,603 *The total profit and lossto date is computed as the net present value of the remaining cashflows; therefore, the value may change each day as the expiration dateapproaches even as the yield does not change. **Value refers to a propersettlement value of the non-biased, centrally cleared swap. ***The totalprofit and loss to date for a cleared swap is the change in thesettlement value of that day plus the accumulated variation margin andcompounded interest earned on the accumulated variation margin. ****Thereturn on the variation margin is computed as the one day financing coston the accumulated variation margin from the previous settlement.

Table 1 shows that the total profit and loss to date of an unclearedswap and that of a non-biased, centrally-cleared swap created pursuantto the principles of the present invention are identical each day.

EXAMPLE 2

This example shows that a non-biased, centrally-cleared financialinstrument in accordance with the present invention can replicate theprofit and loss of a seasoned, uncleared interest-rate swap. The couponof a seasoned interest-rate swap is usually different from the par swaprate when the seasoned swap is traded; to compensate for this, anupfront payment is often made with the amount equal to the present valueof the seasoned swap. As seen in Example 1, the buyer of the 2.0%coupon, spot-starting swap has a marked-to-market loss of $906,603 onday 4 after the yield changed to 2.1%. If the buyer decides to sell theswap on day 4, a loss of $906,603 is incurred, whether the trade is anuncleared swap or a non-biased, centrally-cleared swap future of thepresent invention. The following Table 2 shows the cash flow and profitand loss of the buyer of this seasoned swap:

TABLE 2 Cash Flow and Profit And Loss of Bayer of Seasoned SwapNon-Biased, Centrally-Cleared Uncleared Swap Swap Future Marked-toReturn Total Return on Total Market Cash on Cash P&L to Variation P&L toDate Yield Value Flow* Flow** Date Value Margin Date 4 2.1 −906,603906,603 0 0 −906,497 0 0 5 2.1 −906,655 0 53 0 −906,497 0 0 6 2.1−906,708 0 53 0 −900,497 0 0 *Since the present value of the seasonedswap is negative on day 4, the buyer receives a payment equal to thepresent value, $906,603. **The initial payment generates interest incomefor the buyer each day.

Table 2 shows that the total profit and loss to date of a seasoned,uncleared swap can be replicated by a non-biased, centrally-cleared swapfuture created pursuant to the principles of the present invention, ifthe non-biased, centrally-cleared swap is initiated on the same day asthe uncleared swap.

EXAMPLE 3

This example shows that a non-biased, centrally-cleared financialinstrument in accordance with the present invention can replicate theprofit and loss of an uncleared forward-starting interest-rate swap.Consider the same swap as specified in Example 1—a 10-year swap with$100M notional value with the par. coupon 2.0%. In this example, theswap starting date is one year from the date it is traded. A non-biased,centrally-cleared swap future of the present invention is traded on thesame day. Suppose after 6 months, the yield changes to 2.1. Thefollowing Table 3 shows the cash flow and profit and loss before andafter the yield changes:

TABLE 3 Cash Flow and P&L Before and After Yield Change Non-Biased,Centrally-Cleared Swap Uncleared Swap Return on Total P&L to VariationTotal P&L Date Yield Date Value Margin to Date 180 2.0 0 0 0 0 181 2.1−897,081 −897,082 0 −897,081 182 2.1 −897,133 −897,081 −52 −897,133Table 3 shows that the total profit and loss to date of aforward-starting, uncleared swap can be replicated by a non-biased,centrally-cleared swap future created pursuant to the principles of thepresent invention each day.

EXAMPLE 4

This example compares the economics of a centrally-cleared,interest-rate swap without adjustments for the convexity bias and theNPV Effect (referred to as an unadjusted cleared swap), with anon-biased, centrally-cleared swap in accordance with the presentinvention. The unadjusted cleared swap is assumed to be settled at theproper value each day. Continuing the example set forth in Example 1,when an uncleared swap trades at a yield of 2.0%, a convexity-biased,interest-rate swap future would trade at a higher yield. Assuming theconvexity bias for a 10-year swap is 25 basis points, the equivalent parcoupon of the interest-rate swap future without adjustment for theconvexity bias is 2.25%. Table 4 compares the profit and loss of anon-biased, centrally-cleared swap future of the present invention andan unadjusted cleared swap:

TABLE 4 Profit and Loss after a Yield Change Non-Biased,Centrally-Cleared Swap Future Unadjusted Cleared Swap Coupon = 2 Coupon= 2.25 Return on Total Return on variation P&L to variation Total P&LDate Yield Value margin Date Value margin to Date 1 2.0 0 0 0     0 0 02 2.1 −906,497 0 −906,497 −1,000,000* 0 −1,000,000 3 2.1 −906,497 −53−906,550 −1,000,000  −54 −1,000,054 *The fair settlement value is equalto the sum of the future cash flows.Table 4 shows that the total profit and loss to date of a non-biased,centrally-cleared swap future created pursuant to the principles of thepresent invention is different from that of an unadjusted cleared swapdue to the NPV effect. Furthermore, an unadjusted cleared swap is tradedat a different par coupon from the uncleared swap due to the convexitybias.

EXAMPLE 5

This example shows non-biased swap future in accordance with the presentinvention can replicate the profit and loss of an off-market swap. Anoff-market swap is a swap that has a value other than zero atinitiation. When an off-market swap is traded, the coupon is usually setto be higher or lower than the par swap rate, and an upfront payment ismade between the parties.

Assume a $100M notional value, 10-year, uncleared spot-starting swap istraded when the par yield is 2.0% and the coupon is set to be 3.0%. Thepresent value of this swap is $8,927,737. The corresponding non-biased,centrally-cleared swap future of the present invention is traded withthe same terms. Table 5 shows that the non-biased, centrally-clearedswap future of the present invention replicates the profit and loss ofthis off-market, uncleared swap when the yield changes to 2.1%:

TABLE 5 Cash Flow and Profit and Loss of an Off-Market Swap Non-Biased,Centrally-Cleared Uncleared Swap Swap Future Marked- Return Total Returnon to-Market on Cash P&L to Variation Total P&L Date Yield Value Cashflow Flow Date Value Margin to Date 1 2.0 8,927,737 −8,927,740 0 0 0 0 02 2.1 8,001,468 −496 −926,765 −926,765 0 −926,765 3 2.1 8 001 935 −521−926,819 −926,765 −54 −926,819Table 5 shows that the total profit and loss to date of an off-market,uncleared swap can be replicated by a non-biased, centrally-cleared swapfuture created pursuant to the principles of the present invention eachday.

EXAMPLE 6

An embodiment of a non-biased, centrally-cleared financial instrument inaccordance with the principles of the present invention can trade as aninterest-rate swap future and defines its terminal value according tothe foregoing definition with a constant of 100 added to the futuresprice to be consistent with market convention. In this example, thisembodiment will be referred to as the “total-return swap future”. Theinitial price of a swap future with a par coupon is 100.

In this example, the total-return swap future is compared with aninterest-rate swap cleared through IDCG. Two points are highlightedthrough this comparison. First, as a main feature of the IDCGinterest-rate swap, fixed and floating coupon payments, as defined bythe terms of the swap, are exchanged bilaterally when they become due.The total-return swap future replicates the economic effect of thecoupon payments without requiring bilateral payments by having thedefinition of terminal value include the net accumulation of cash flows.Second, since the IDCG swap generates daily variation margin, withoutappropriate adjustment, the total profit and loss on the IDCG swap isnot equivalent to an uncleared swap as a result of both the convexitybias and the NPV effect.

Assume two different 10-year spot starting par swaps with a notionalvalue of $100M as in Example 1 are traded as a total-return swap futureand on IDCG simultaneously. Both are centrally cleared. The par couponof the total-return swap future is 2.0%, equal to the prevailing yield.For the purpose of comparison, assume the IDCG cleared swap is traded atthe same coupon.

To show that the total-return swap future replicates the economic effectof the coupon payments without requiring bilateral payments, Table 6acompares the cash flow and the profit and loss of the total-return swapfuture with the IDCG cleared swap before and after a payment is duepursuant to the terms of the swap. Assuming the yield does not changefrom day 1 to day 90, a floating payment of $500,000 is payable from thebuyer to the seller.

TABLE 6a IDCG Cleared Swap Total-Return Swap Future Coupon = 2 Coupon =2 Accum. Marked Interest to Accum. on Total Settle- Return on TotalMarket Coupon Variation 'Coupon P&L to ment Variation P&L to Date YieldValue Payment Margin Payment Date Price Margin Date 90 2.0 500,000−500,000 0 0 0 100 0 0 91 2.0 500,028 28 −28 0 100 0 0Table 6a shows that the total profit and loss to date of a total-returnswap future is the same as that of an IDCG cleared swap withoutrequiring bilateral coupon payments.

To demonstrate that the IDCG cleared swap without appropriate adjustmentis not equivalent to an uncleared swap, assume the yield changes to 2.1%on day 92. Table 6b compares the cash flows and profit and loss of theIDCG cleared swap and the total return swap future:

TABLE 6b Comparison of IDCG Cleared Swap and Total Return Swap Futureafter Yield Change IDCG Cleared Swap Total-Return Swap Future Coupon = 2Coupon = 2 Accum. Interest Return Marked to Accum. on - Tot-1 Settle- onTotal Market Coupon Variation Coupon P&L to ment Variation P&L to DateYield Value Payment Margin Payment Date Price Margin Date 92 2.1−417,744 −917,744 −57 −917,800 99.0822 0 −917,800 93 2.1 −417,768−917,822 −86 −917,908 99.0822 −54 −917,854Table 6b shows that the total profit and loss to date on the IDCGcleared swap is different from that of the total return swap future. Asalready seen from previous examples, the non-biased, centrally-clearedswap future created in accordance to the principles of the presentinvention is economically equivalent to an uncleared swap. Therefore theIDCG cleared swap, without proper adjustments, does not generate thesame profit and loss as an uncleared swap. The reason for thisdiscrepancy in the total profit and loss to date is because all of thechanges in net present value of the IDCG swap flow to and from the buyerthrough variation margin, causing the NPV effect to be present. Andfurther, because the accumulated variation margin accrues interest at arate that is correlated with the marked-to-market value of the IDCGswap, the convexity bias is also partly responsible for the discrepancyin the profit and loss.

EXAMPLE 7

The following example illustrates the NPV effect in the case of acleared credit default swap (CDS) without adjustment. Consider twocounterparties enter into a $10M notional value, 5-year CDS with XYZCorp as the reference entity, at a premium of 500 basis points of thenotional amount per annum (known as the spread). This obligates thebuyer to pay $125,000 ($10M*5.0%/4) to the seller every quarter for 5years, or until the default of XYZ Corp if the default occurs before thematurity of the CDS. In return, the buyer will receive $10M if XYZ Corpdefaults within the 5-year period of the CDS. To simplify this example,the default risk of XYZ Corp is assumed to be uncorrelated with interestrates; that being the case, a cleared CDS would have traded at the samespread (i.e. 500 basis points) in the absence of convexity bias. Assumethat immediately after the trade is consummated, the market assessmentof the default risk of XYZ Corp changes, and the spread of a 5-year XYZCorp CDS is now 300 basis points. The following will compare the profitand loss between an uncleared CDS, a cleared CDS without adjustment forthe NPV effect, and a non-biased, centrally-cleared financial instrumentcreated in accordance with the principles of the current invention.

In the case of an uncleared CDS, the marked-to-market value of theoriginal CDS with 500 basis point spread is equal to the sum of thepresent value of a stream of −$50,000 ($10M*(−5.0%+3.0%)/4) quarterlypayments until the maturity of the CDS or the default of XYZ Corp,whichever comes first, or approximately −$758,432 assuming an interestrate of 6.0% and a certain probability of default. If the buyer unwindsthe position at that time, a loss of −$758,432 is realized.

Consider a cleared CDS without adjustment where the exchange or theclearinghouse requires the daily settlement to be equal to the netpresent value of an uncleared CDS. Since the net present value of theCDS at the end of day one is −$758,432, a loss of the same amount occursto the buyer through the variation margin. However, even after thevariation margin flows, the buyer needs to pay a certain amount tounwind the position. To see this, consider a third party “buys” this CDSfrom the original buyer with no payment. The credit risk can be hedgedby selling a new CDS at the spread of 300 basis points with the samenotional value and maturity. The net marked-to-market value of long aCDS at 500 basis points and short a CDS at 300 basis points willdecrease from −$758,432 to −$1,000,000 (−$50,000*4*10), if the defaultdoes not occur before the maturity, and otherwise to a value between−$758,432 and −$1,000,000. The present value of this stream of negativecash flow is approximately −$153,334, which is the fair price that theoriginal buyer has to pay to the third party to unwind its position. Thetotal loss from trading this cleared CDS is thus significantly more thanthat from trading the uncleared CDS. This is caused by the NPV effect.

Now consider the non-biased, centrally-cleared financial instrumentcreated in accordance with the principles of the present invention. Onday one, after the CDS spread changes to 300 basis points, the fairsettlement value will be equal to the net present value of the unclearedCDS, i.e., −$758,432. The buyer can unwind its position by entering ashort position in a new CDS with the spread of 300 basis points and thesame notional value and maturity. The terminal value of these long andshort positions, in accordance with the present invention, is equal tothe accumulated value of a stream of −$50,000 paid quarterly until thematurity of the CDS or the default of XYZ Corp, whichever comes first,minus the accumulated value of all the interest paid for this stream ofnegative cash flows. Therefore, the terminal value is equal to thepresent value of this stream of negative cash flows, or −$758,432. Thebuyer will have no additional profit or loss, and the loss of $758,432is locked in on day one. Thus, the centrally-cleared financialinstrument has the same economic effect as the uncleared CDS when theCDS spread changes.

This concludes the Examples of non-biased, centrally-cleared financialinstruments created by adjusting the terminal value for the interest onvariation margin in accordance with the principles of the presentinvention.

A non-biased, centrally-cleared financial instrument in accordance withthe principles of the present invention may be transacted by a varietyof means, including but are not limited to a trading floor, telephone orelectronically. After the trade has been agreed to by the buyer andseller, whether it is in a private communication or a publiclyaccessible medium, a financial instrument of the present invention willthen be submitted to a clearinghouse for central clearing. A furtheraspect of the present invention relates to the electronic clearing andsettling of such non-biased, centrally-cleared financial instruments.

In accordance with the principles of the present invention, on aperiodic, generally daily basis, the exchange or clearinghouse maydetermine and publish a settlement price for a non-biased,centrally-cleared financial instrument. The settlement price of thenon-biased, centrally-cleared financial instrument is determined by themarket price at which the non-biased, centrally-cleared financialinstrument is quoted or traded on each day. In the case where a marketprice is not directly observed, the non-biased, centrally-clearedfinancial instrument should be settled at a value that is consistentwith other related financial instruments whose market prices areobservable. In such case, the financial instrument can be settled at avalue equal to a sum of present value of remaining asset flows, plusaccumulated value of past asset flows, minus accumulated return onvariation margin.

Take a non-biased, centrally-cleared, interest-rate swap as an example;if a non-biased, centrally-cleared swap created according to the presentinvention does not have a market price on a particular day, the exchangeor clearinghouse will settle the interest-rate swap to a value equal tothe sum of the present value of remaining cash flows, plus theaccumulated value of past cash flows, minus the accumulated total returnon variation margin to date. The evaluation of cash flows utilizes ayield curve constructed using other liquid, interest-rate swaps orinterest-rate financial instruments; therefore, consistency with thevalue of a liquid, non-biased, centrally-cleared, interest-rate swap isguaranteed.

The following is a non-limiting example of a daily settlementmethodology implemented for a centrally-cleared interest-rate swap inaccordance with the principles of the current invention.

EXAMPLE 8

Consider the 10-year interest-rate swap set forth in Example 1. On theday the trade is consummated, the non-biased, centrally-cleared swap issettled to its present value according to the following standardpractice of valuing interest-rate swaps: First, a yield curve is builtfrom the current cash deposit rates, LIBOR, Eurodollar futures, and swaprates for a list of key maturities: 3 year, 4 year, 5 year, 10 year, 15year, 20 year, and 30 year. Using a “bootstrapping” method, the yieldcurve is constructed from those rates or instruments.

Second, the present value of the fixed leg is computed as:

${{PV}_{fixed} = {C \times P \times {\sum\limits_{i = 1}^{M}\left( {\frac{t_{i}}{T_{i}} \times {df}_{i}} \right)}}},$

where P is the notional amount, C is the fixed coupon of the swap, M isthe number of the fixed payments, t_(i) is the number of days in periodi, T_(i) is the basis according to the day count convention, and df_(i)is the discount factor derived from the yield curve constructed as abovefor the i^(th) fixed coupon payment. Third, the present value of thefloating leg is computed as:

${{PV}_{float} = {P \times {\sum\limits_{j = 1}^{N}\left( {f_{j} \times \frac{t_{j}}{T_{j}} \times {df}_{j}} \right)}}},$

where N is the number of the floating payments and f_(j) is the forwardrate for the time period j. Finally, the present value of the swap iscomputed as PV_(fixed)−PV_(float).

A non-biased, centrally-cleared, interest-rate swap with the par couponof 2.0% as in Example 1 is settled at 0 on day 1.

On day 2, assume the yield curve shifts upwards by 10 basis points. Thesettlement value of this non-biased, centrally-cleared interest-rateswap is computed as the present value of remaining cash flows of theswap, plus the accumulated value of past cash flows, minus theaccumulated total return on variation margin to date. The present valueof remaining cash flows is equal toPV_(fixed)−PV_(float)=$9,093,503-$10,000,000=−$906,497. The accumulatedvalue of past cash flow is 0 as no coupon payment has been made, and theaccumulated total return on variation margin is 0 since no variationmargin has been generated since the initial trading day. Therefore thesettlement value of the non-biased, centrally-cleared interest rate swapis equal to −$906,497 on day 2.

On day 3, assume there has been no change in the yield curve since day2. The present value of remaining cash flows is equal toPV_(fixed)−PV_(float)=$9,093,450−$10,000,000=−$906,550. The accumulatedvalue of past cash flows is still 0. The accumulated total return onvariation margin, currently −$906,497, is equal to the −$53(−$906,497*2.1%/365). Therefore, the settlement value on day 3 is equalto $−906,497 (−$906,550−(−$53)).

The non-biased, centrally-cleared financial instrument may be marked tomarket, generally daily, using its settlement price. On the same timescale that a settlement value is published, generally daily, theclearinghouse can compute the variation margin requirement for eachnon-biased, centrally-cleared financial instrument. Cash flow paymentsreflecting the variation margins will flow between the clearinghouse andparties holding open positions in non-biased, centrally-clearedfinancial instruments on a periodic, generally daily basis.

The clearinghouse must store and maintain the historical data series ofdaily settlement values for each financial instrument, as well as theovernight interest rate. These, in addition to the initial trade price,are required for determining the terminal value and may be stored in adatabase and can be published to the marketplace.

On the last day of the existence of the non-biased, centrally-clearedfinancial instrument, generally known as expiration, the clearing housewill compute and settle the non-biased, centrally-cleared financialinstrument to the terminal value as defined according to the principlesof the present invention. As previously described, in one example anon-biased, centrally-cleared financial instrument of the presentinvention can be cleared and settled utilizing a terminal valuedetermined in accordance with the previously detailed alternativeembodiments.

According to the principles of this invention, in order to publish dailyand terminal settlement values, a clearinghouse, exchange, futurescommission merchant or other market participant may use computers withsoftware specifically designed for this purpose. The computation of theterminal value in accordance with the present invention is iterative andcomplex, and special software is required for this purpose. Thissoftware may be linked to a centralized marketplace via data lines,networks or the Internet, so that the prices are published in a seamlessmanner. The clearing house may store the daily prices for each financialinstrument in existence at any given moment in a database and can beelectronically published to the marketplace.

Referring to FIG. 3, a non-limiting example of a high level hardwareimplementation can used to run a system of the present invention isseen. The infrastructure should include but not be limited to: wide areanetwork connectivity, local area network connectivity, appropriatenetwork switches and routers, electrical power (backup power), storagearea network hardware, server-class computing hardware, and an operatingsystem such as for example Redhat Linux Enterprise AS Operating Systemavailable from Red Hat, Inc, 1801 Varsity Drive, Raleigh, N.C.

The clearing and settling and administrative applications softwareserver can run for example on an HP ProLiant DL 360 G6 server withmultiple Intel Xeon 5600 series processors with a processor basefrequency of 3.33 GHz, up to 192 GB of RAM, 2 PCIE expansion slots, 1 GBor 10 GB network controllers, hot plug SFF SATA drives, and redundantpower supplies, available from Hewlett-Packard, Inc, located at 3000Hanover Street, Palo Alto, Calif. The database server can be run forexample on a HP ProLiant DL 380 G6 server with multiple Intel Xeon 5600series processors with a processor base frequency of 3.33 GHZ, up to 192GB of RAM, 6 PCIE expansion slots, 16 SFF SATA drive bays, an integratedP410i integrated storage controller, and redundant power supply,available from Hewlett-Packard.

While the invention has been described with specific embodiments, otheralternatives, modifications, and variations will be apparent to thoseskilled in the art. Accordingly, it will be intended to include all suchalternatives, modifications and variations set forth within the spiritand scope of the appended claims.

What is claimed is:
 1. A non-biased financial instrument comprising: aterminal value such that the terminal value offsets co-movement ofvariation margin and investment return on the variation margin; thefinancial instrument being centrally cleared; whereby the convexity biasor the NPV effect or both are addressed.
 2. The non-biased financialinstrument of claim 1 further wherein the terminal value comprises anaccumulated value of payments made pursuant to the terms of thefinancial instrument, minus the accumulated interest earned on variationmargin for the life of the financial instrument.
 3. The non-biasedfinancial instrument of claim 2 further wherein the financial instrumentis a swap and the terminal value is derived in accordance with:terminal  value = net  accumulated  value  of  cash  flow − total  return  on  variation  margin;where, net accumulated value of cash flow is the accumulated value thata buyer (seller) of a swap receives minus the payments the buyer(seller) makes, reinvested at the overnight rate from the date that thecash flow occurs to expiration of the swap; total return on variationmargin is the sum of the interest earned on the cumulative variationmargin for each day reinvested at the overnight rate to expiration ofthe swap; and the overnight rate is the rate specified by the exchangeor clearinghouse to reflect the short-term financing rate of marketparticipants.
 4. The non-biased financial instrument of claim 3 furtherwherein the net accumulated value of cash flow is derived in accordancewith:${{net}\mspace{14mu}{accumulated}\mspace{14mu}{value}\mspace{14mu}{of}\mspace{14mu}{cash}\mspace{14mu}{flows}} = {{\sum\limits_{i = 1}^{N}{C_{i}{B\left( {t_{c,i},T} \right)}}} - {\sum\limits_{i = 1}^{M}{L_{i}{B\left( {t_{l,i},T} \right)}}}}$where, C_(i) is the amount of fixed leg payment payable at time t_(c,i);L_(i) is the amount of the floating leg payment payable at time t_(i,j);T is the expiration of the swap; and B(t,T) is the value of the moneymarket account at time T with an initial deposit of 1 at time t andaccumulated at the overnight rate.
 5. The non-biased financialinstrument of claim 3 further wherein the total return on variationmargin is determined as:${{{total}\mspace{14mu}{return}\mspace{14mu}{on}\mspace{14mu}{variation}\mspace{14mu}{margin}} = {\sum\limits_{t = 1}^{T - 1}{P_{t}R_{t}{B\left( {{t + 1},T} \right)}}}},$where P_(t) is the settlement price of the swap on day t, and R_(t) isthe overnight interest rate on day t.
 6. The non-biased financialinstrument of claim 2 further wherein the financial instrument is a swapand the terminal value is derived in accordance with:terminal  value = net  summation  of  cash  flows − total  return  on  modified  variation  margin,where, using the previous notations,${{{net}\mspace{14mu}{summation}\mspace{14mu}{of}\mspace{14mu}{cash}\mspace{14mu}{flows}} = {{\sum\limits_{i = 1}^{N}C_{i}} - {\sum\limits_{i = 1}^{M}L_{i}}}};{{{and}\mspace{14mu}{total}\mspace{14mu}{return}\mspace{14mu}{on}\mspace{14mu}{modified}\mspace{14mu}{variation}\mspace{14mu}{margin}} = {\sum\limits_{i = 1}^{l - 1}{\left( {P_{i} - \left( {{\sum\limits_{i:{({t_{c,i} < t})}}C_{i}} - {\sum\limits_{i:{({t_{l,i} < t})}}L_{i}}} \right)} \right)R_{t}{B\left( {{t + 1},T} \right)}}}}$7. The non-biased financial instrument of claim 1 further wherein thefinancial instrument is selected from the group consisting ofinterest-rate swaps, interest-rate swap futures, credit default swaps,credit default swap futures, other interest-rate futures, FRAs,commodity swaps, and foreign-exchange swaps.
 8. The non-biased financialinstrument of claim 1 further wherein the financial instrument isexchange-traded.
 9. The non-biased financial instrument of claim 1further wherein the financial instrument is not exchange-traded.
 10. Thenon-biased financial instrument of claim 1 further wherein the financialinstrument is electronically traded.
 11. The non-biased financialinstrument of claim 1 further wherein there is a correlation between thevalue of the financial instrument and interest rates.
 12. The non-biasedfinancial instrument of claim 1 further having a constant added orsubtracted to the price or rate applicable to the financial instrument.13. The non-biased financial instrument of claim 1 further having anexpiration date being the maturity date of the financial instrument. 14.The non-biased financial instrument of claim 1 further wherein thefinancial instrument is cash settled.
 15. The non-biased financialinstrument of claim 1 further wherein the financial instrument isphysically settled.
 16. The non-biased financial instrument of claim 1further wherein the financial instrument is denominated in United Statesdollars.
 17. The non-biased financial instrument of claim 1 furtherwherein the non-biased financial instrument is traded on Eris Exchange.18. The non-biased financial instrument of claim 1 further wherein theterminal value offsets the total co-movement of variation margin andinvestment return on the variation margin of the financial instrument.19. The non-biased financial instrument of claim 1 further wherein thefinancial instrument is settled at a value equal to a sum of presentvalue of remaining asset flows, plus accumulated value of past assetflows, minus accumulated return on variation margin.
 20. A computerprogram product, comprising a computer usable medium having a computerreadable program code embodied therein, the computer readable programcode adapted to be executed to implement a method for clearing andsettling a non-biased financial instrument, the method comprising:providing a non-biased financial instrument having a terminal value suchthat the terminal value offsets co-movement of variation margin andinvestment return on the variation margin; and centrally clearing thefinancial instrument; whereby the convexity bias or the NPV effect orboth are addressed.
 21. The computer program product of claim 20 furthercomprising providing a non-biased swap having a terminal valuecomprising an accumulated value of payments made pursuant to the termsof the swap, minus the accumulated value of interest earned on variationmargin for the life of the swap.
 22. The computer program product ofclaim 21 further comprising providing a non-biased swap having aterminal value derived in accordance with:terminal  value = net  accumulated  value  of  cash  flow − total  return  on  variation  margin;where, net accumulated value of cash flows is the accumulated value thata buyer (seller) of a swap receives minus the payments the buyer(seller) makes, reinvested at the overnight rate from the date that thecash flow occurs to expiration of the swap; total return on variationmargin is the sum of the interest earned on the cumulative variationmargin for each day reinvested at the overnight rate to expiration ofthe swap; and the overnight rate is the rate specified by the exchangeor clearinghouse to reflect the short-term financing rate of marketparticipants.
 23. The computer program product of claim 22 furthercomprising providing a non-biased swap having a net accumulated value ofcash flow derived in accordance with:${{net}\mspace{14mu}{accumulated}\mspace{14mu}{value}\mspace{14mu}{of}\mspace{14mu}{cash}\mspace{14mu}{flows}} = {{\sum\limits_{i = 1}^{N}{C_{i}{B\left( {t_{c,i},T} \right)}}} - {\sum\limits_{i = 1}^{M}{L_{i}{B\left( {t_{l,i},T} \right)}}}}$where, C_(i) is the amount of fixed leg payment payable at time t_(c,i);L_(i) is the amount of the floating leg payment payable at time t_(i,j);T is the expiration of the swap; and B(t,T) is the value of the moneymarket account at time T with an initial deposit of 1 at time t andaccumulated at overnight rate.
 24. The computer program product of claim22 further comprising providing a non-biased swap having a total returnon variation margin determined as:${{{total}\mspace{14mu}{return}\mspace{14mu}{on}\mspace{14mu}{variation}\mspace{14mu}{margin}} = {\sum\limits_{t = 1}^{T - 1}{P_{t}R_{t}{B\left( {{t + 1},T} \right)}}}},$where P_(t) is the settlement price of the swap on day t, and R_(t) isthe overnight interest rate of on day t.
 25. The computer programproduct of claim 21 further wherein the financial instrument is a swapand the terminal value is derived in accordance with:terminal  value = net  summation  of  cash  flows − total  return  on  modified  variation  margin,where, using the previous notations,${{{net}\mspace{14mu}{summation}\mspace{14mu}{of}\mspace{14mu}{cash}\mspace{14mu}{flows}} = {{\sum\limits_{i = 1}^{N}C_{i}} - {\sum\limits_{i = 1}^{M}L_{i}}}};{{{and}\mspace{14mu}{total}\mspace{14mu}{return}\mspace{14mu}{on}\mspace{14mu}{modified}\mspace{14mu}{variation}\mspace{14mu}{margin}} = {\sum\limits_{t = 1}^{T - 1}{\left( {P_{t} - \left( {{\sum\limits_{i:{({t_{c,i} < t})}}C_{i}} - {\sum\limits_{i:{({t_{l,i} < t})}}L_{i}}} \right)} \right)R_{t}{B\left( {{t + 1},T} \right)}}}}$26. A general-purpose digital computer programmed to carry out a seriesor steps, the series of steps to electronically clear and settle anon-biased financial instrument comprising: providing a non-biasedfinancial instrument having a terminal value such that the terminalvalue offsets co-movement of variation margin and investment return onthe variation margin; and centrally clearing the financial instrument;whereby the convexity bias or the NPV effect or both are addressed. 27.The general-purpose digital computer of claim 26 further comprisingproviding a non-biased swap having a terminal value comprising anaccumulated value of payments made pursuant to the terms of the swap,minus the accumulated value of interest earned on variation margin forthe life of the swap.
 28. A non-biased financial instrument obtained bya process, the process comprising: providing a financial instrumenthaving a terminal value such that the terminal value offsets co-movementof variation margin and investment return on the variation margin; andcentrally clearing the financial instrument; whereby the convexity biasor the NPV effect or both are addressed
 29. The non-biased financialinstrument obtained by a process of claim 28 further comprisingproviding a swap having a terminal value comprising an accumulated valueof payments made pursuant to the terms of the swap, minus theaccumulated value of interest earned on variation margin for the life ofthe swap.
 30. A non-biased financial instrument comprising: means forproviding a financial instrument having a terminal value; and means forproviding the terminal value such that co-movement of variation marginand investment return on the variation margin are offset; and means forcentrally clearing the financial instrument; whereby the convexity biasor the NPV effect or both are addressed.
 31. The non-biased financialinstrument of claim 30 further comprising means for providing a swap andmeans for providing a terminal value comprising an accumulated value ofpayments made pursuant to the terms of the swap, minus the accumulatedvalue of interest earned on variation margin for the life of the swap.32. A method of electronically clearing and settling a non-biasedfinancial instrument comprising: electronically providing on a processora financial instrument having a terminal value such that the terminalvalue offsets co-movement of variation margin and investment return onthe variation margin; and electronically centrally clearing and settlingthe financial instrument on a processor; whereby the convexity bias orthe NPV effect or both are addressed.
 33. The method of electronicallyclearing and settling a non-biased financial instrument of claim 32further electronically providing on a processor a swap having a terminalvalue comprising an accumulated value of payments made pursuant to theterms of the swap, minus the accumulated value of interest earned onvariation margin for the life of the swap.
 34. A method of clearing andsettling a financial instrument comprising settling the financialinstrument at a value equal to a sum of present value of remaining assetflows, plus accumulated value of past asset flows, minus accumulatedreturn on variation margin.
 35. The method of clearing and settling afinancial instrument of claim 34 further including settling thefinancial instrument to a value equal to a sum of present value ofremaining cash flows, plus accumulated value of past cash flows, minusaccumulated return on variation margin.
 36. The method of clearing andsettling a financial instrument of claim 34 further including settlingan interest-rate swap to a value equal to a sum of present value ofremaining cash flows, plus accumulated value of past cash flows, minusaccumulated return on variation margin.
 37. The method of clearing andsettling a financial instrument of claim 36 further including utilizinga yield curve constructed using other liquid, interest-rate swaps orinterest-rate financial instruments for the evaluation of cash flows.38. The method of clearing and settling a financial instrument of claim34 further including marking to market the financial instrument usingits settlement price.
 39. The method of clearing and settling afinancial instrument of claim 34 further including computing a variationmargin requirement for financial instrument.
 40. The method of clearingand settling a financial instrument of claim 34 further includingdetermining a terminal value of the financial instrument as anaccumulated value of payments made pursuant to the terms of thefinancial instrument, minus the accumulated interest earned on variationmargin for the life of the financial instrument.
 41. The method ofclearing and settling a financial instrument of claim 34 furtherincluding selecting the financial instrument from the group consistingof interest-rate swaps, interest-rate swap futures, credit defaultswaps, credit default swap futures, other interest-rate futures, FRAs,commodity swaps, and foreign-exchange swaps.
 42. The method of clearingand settling a financial instrument of claim 34 further includingsettling the financial instrument in United States dollars.
 43. Themethod of clearing and settling a financial instrument of claim 34further including cash settling the financial instrument.
 44. The methodof clearing and settling a financial instrument of claim 34 furtherincluding physically settling the financial instrument.